you and 50 coworkers decide to play a game that consists of flipping a coin once for each coworker. If the flip coin for the particular coworker results in a head, you have to pay them $1. If it results in tail, neither party has to pay anything. Given the information provided above, and assuming that the coin you are using is a far coin (i.e. the probability of getting a head or a is equal to 0.5) use Microsoft excel, as your graphing calculator, or the binomial probability formula to calculate the probibilities of the following events. Event A: The probability that you will have to oay out exactly $20. (In other words, the probability that 20 of the flips of the coin will result in heads.) Event B: The probability that you will not have to pay anyone anything. (In other words, the probability that none of the flips of the coin will result in heads.
the probability is 0
To calculate the probabilities of Event A and Event B using the binomial probability formula, we need to determine the number of trials, the probability of success, and the desired number of successes. In this case:
Number of trials (n) = 50 (the number of coworkers)
Probability of success (p) = 0.5 (the probability of getting heads)
Desired number of successes:
- Event A: 20 (the number of coworkers you have to pay)
- Event B: 0 (the number of coworkers you have to pay)
Let's calculate each probability step-by-step:
Event A: The probability that you will have to pay out exactly $20.
1. Open Microsoft Excel and choose an empty cell (e.g., A1) to enter the formula.
2. Enter the formula: =BINOM.DIST(20,50,0.5,FALSE)
- The first argument (20) is the desired number of successes.
- The second argument (50) is the total number of trials.
- The third argument (0.5) is the probability of success.
- The fourth argument (FALSE) specifies that we're looking for a precise number of successes.
3. Press Enter to get the result.
- The result will be the probability of getting exactly 20 heads in 50 flips.
Event B: The probability that you will not have to pay anyone anything.
1. Choose another empty cell (e.g., A2) to enter the formula.
2. Enter the formula: =BINOM.DIST(0,50,0.5,FALSE)
- The first argument (0) is the desired number of successes.
- The second argument (50) is the total number of trials.
- The third argument (0.5) is the probability of success.
- The fourth argument (FALSE) specifies that we're looking for a precise number of successes.
3. Press Enter to get the result.
- The result will be the probability of getting 0 heads in 50 flips.
By following these steps, you can use Microsoft Excel as a graphing calculator to calculate the probabilities of Event A and Event B.
To calculate the probabilities of the events described using Microsoft Excel, you can use the binomial probability formula. The formula for calculating the probability of exactly "k" successes (heads in this case) in "n" trials with a success probability of "p" is:
P(X=k) = (n C k) * p^k * (1-p)^(n-k)
Here's how you can use Microsoft Excel to calculate these probabilities:
1. Open Microsoft Excel and set up your worksheet. In cell A1, enter the label "Number of Heads." In cell B1, enter the label "Probability." In cells A2 to A51, enter the numbers 0 to 50 to represent the number of heads. In cell B2, enter the formula to calculate the probability of getting exactly 0 heads:
=BINOM.DIST(0,50,0.5,FALSE)
2. Click on cell B2 and drag the fill handle (the small square at the bottom right corner of the cell) down to cell B51. This will calculate the probabilities for getting 0 to 50 heads.
3. To calculate the probability of event A (exactly 20 heads), go to cell C1 and enter the label "Event A probability." In cell C2, enter the formula:
=BINOM.DIST(20,50,0.5,FALSE)
This will calculate the probability of getting exactly 20 heads.
4. To calculate the probability of event B (no heads), go to cell D1 and enter the label "Event B probability." In cell D2, enter the formula:
=BINOM.DIST(0,50,0.5,FALSE)
This will calculate the probability of getting no heads.
Now, cell B2 to B51 will display the probabilities of getting 0 to 50 heads, cell C2 will display the probability of event A, and cell D2 will display the probability of event B.
You can format the cells as percentages if you'd like to see the probabilities in that format. Select the cells, go to the "Home" tab, click on the "Number Format" dropdown, and choose the percentage format.
Remember that using the binomial probability formula directly in Excel will give you the exact probabilities based on the assumptions given, assuming that the coin is fair (0.5 probability for heads and tails).